Journal of Statistical Physics

, Volume 84, Issue 5–6, pp 987–1041 | Cite as

Markov chains with exponentially small transition probabilities: First exit problem from a general domain. II. The general case

  • E. Olivieri
  • E. Scoppola
Articles

Abstract

In this paper we consider aperiodic ergodic Markov chains with transition probabilities exponentially small in a large parameter β. We extend to the general, not necessarily reversible case the analysis, started in part I of this work, of the first exit problem from a general domainQ containing many stable equilibria (attracting equilibrium points for the β=∞ dynamics). In particular we describe the tube of typical trajectories during the first excursion outsideQ.

Key Words

Markov chains first exit problem large deviations 

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • E. Olivieri
    • 1
  • E. Scoppola
    • 2
  1. 1.Dipartimento di MatematicaUniversità di Roma Tor VergataRomeItaly
  2. 2.Dipartimento di MatematicaTerza Università di RomaRomeItaly

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